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Whitehead A.N. — A Treatise on Universal Algebra with Applications, Vol. 1
Whitehead A.N. — A Treatise on Universal Algebra with Applications, Vol. 1

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Название: A Treatise on Universal Algebra with Applications, Vol. 1

Автор: Whitehead A.N.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1898

Количество страниц: 586

Добавлена в каталог: 19.06.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Absolute in connection with Congruent Transformations      456 sqq 500
Absolute in connection with Conic Section, defined      497;
Absolute in connection with Plane      367 496
Absolute in connection with Point-pair, defined      351;
Absolute in connection with Points on, in Hyperbolic Geometry      422;
Absolute in connection with Polar Begions      367 384 420;
Absolute in connection with Quadric, defined      355
Absorption, Law of      36 sqq.
Acceleration in Euclidean Space      540 xqq.;
Acceleration in Non-Euclidean Space      482 sqq
Addition and Multiplication      25 sqq.
Addition and Positional Manifolds      120 sqq.
Addition in Algebra of Symbolic Logic      35 sqq.
Addition in connection with Classification of Algebras      29 sqq.;
Addition of vectors      507 sqq.
Addition, Principles of, in Universal Algebra, defined      19 sqq.
Addition, Relations      123
Algebra, Linear, and Algebra of Symbolic Logic      35
Algebra, Linear, defined      28
Algebra, Linear, mentioned      32 172;
Algebra, Universal, defined      18.
Algebra, Universal, mentioned      11 35
Algebras, classification of      29 sqq.
Algebras, Linear Associative      30
Algebras, Numerical Genus of      29 119
Algebras, Species of, defined      27
Angle of Contingence and      552;
Angle of Contingence, in Euclidean Space      539
Angle of Contingence, in Non-Euclidean Space      479;
Angle of Parallelism, in Hyperbolic Space      438
Angle of Torsion, in Euclidean Space      540;
Angle of Torsion, in Non-Euclidean Space      479
Angular Distance between Points in Anti-space      417
Anharmonic Ratio in Positional Manifolds, defined      132;
Anharmonic Ratio of Systems of Forces      290.
Anti-space, considered      414 sqq.;
Anti-space, defined      354
Anti-spatial Elements      414 sqq.
Antipodal Elements, defined      166;
Antipodal Elements, in Elliptic Space      361
Antipodal Form of Elliptic Geometry, defined      355;
Antipodal Intercept, defined      168;
Antipodal Intercept, length of      362
Arbitrary Regions in Algebra of Symbolic Logic      55 sqq.
Arithmetic and Algebra      11
Associated Quadric of Triple Group      see Group; System of Forces see
Associative Law and Algebra of Symbolic Logic      37;
Associative Law and Combinatorial Multiplication      174
Associative Law and Matrices      251;
Associative Law and Multiplication      27;
Associative Law and Pure and Mixed Products      185;
Associative Law and Steps      25;
Associative Law, defined      21
Ausdehnungslehre      13 19 32 115 131 168 171 172 180 198 210 219 229 248 262 278 317 522 573.
Axis of a Congruent Transformation in Elliptic Space      471;
Axis of a Congruent Transformation in Euclidean Space      501
Axis of a Congruent Transformation in Hyperbolic Space      458
Axis of a Dual Group      see Group.
Axis, Central, in Elliptic Geometry      401;
Axis, Central, in Euclidean Geometry      529
Axis, Central, in Hyperbolic Geometry      454
Ball, Sir B.S.      281 370 406 462 473 475 531 532
Base point      518
Beltrami      369 451
Binomial Expressions in Symbolic Logic      45 sqq.
Biquaternions      370 398.
Bolyai, J.      369 426 436 451 487;
Bolyai, J., Wolfgang      369.
Boole      4 10 35 46 63 96 111 115 116
Bradley      6 10
Brianchon's theorem      231
Buchheim      248 253 254 278 370 405 575.
Burali — Forti      522 575
Burnside      370.
Calculus, General Nature of, denned and discussed      4 sqq.;
Calculus, General Nature of, of Extension, Algebraic Species of      28 31
Calculus, General Nature of, of Extension, and Descriptive Geometry      132 214
Calculus, General Nature of, of Extension, and Theory of Duality      146 196 212 481;
Calculus, General Nature of, of Extension, investigated      169 sqq.
Cantor, G.      16.
Carried Functions      569 sqq.
Cayley      119 131 135 161 248 249 351 352 353 354 369
Central Axis      see Axis.
Central Plane of Sphere in Hyperbolic Geometry      442.
Centre of Dual Group      see Group.
Characteristic Lines of Congruent Transformation      470
Characteristics of a Manifold      13
Characteristics of a Scheme      9 14;
Chasles      246.
Circle, defined, and Perimeter of, in Elliptic Geometry      375;
Circle, Great, on Sphere in Hyperbolic Geometry      448
Circle, on Sphere in Hyperbolic Geometry      484.
Classification (operation in Symbolic Logic)      41
Clebsch      369 569 570;
Clebsch and Lindemann      278 280 294
Clifford      13 369 370 398 406t 409 472
Co-ordinate Elements, defined      125;
Co-ordinate Region, defined      126
Co-ordinates, Conjugate, denned      148.
Co-ordinates, Curvilinear, in Euclidean Space      543;
Co-ordinates, Curvilinear, in Non-Euclidean Space      488 494;
Combination, General Definition of      8
Common Null Line of a Group      286
Commutative Law and Algebra of Symbolic Logic      37;
Commutative Law and Congruent Transformations      464;
Commutative Law and Multiplication      27
Commutative Law, defined      21.
Complete Manifold, defined      15
Complex Intensity      120.
Complexes, Conjunctive and Disjunctive, defined and discussed      107 sqq.;
Complexes, Linear      278 sqq.
Compound Extensive Magnitudes, denned      177 sqq.
Congruence of Terms, defined      122
Congruences of Lines and Dual Groups      288
Congruent Ranges, defined      350;
Congruent Ranges, Klein's Theorem concerning      353
Congruent Transformations and Work      469 477 537
Congruent Transformations in Euclidean Geometry      500 sqq. 53Qsqq.;
Congruent Transformations in Non-Euclidean Geometry      456 sqq.;
Congruent Transformations, Associated Systems of Forces of      466 476 536
Congruent Transformations, Parameters of      460 471
Conies, Descriptive Geometry of      229 sqq
Conjugate Co-ordinates, defined and discussed      148sqq.
Conjugate lines      277;
Conjugate Sets of Systems of Forces      298 306 308.
Conjunctive Complex      107 sqq
Construction in a Positional Manifold, defined      214;
Construction, Grassmann's      219 sqq.;
Construction, Linear, of Cubics      233 sqq.;
Construction, von Staudt's      215 sqq
Content, Theory of      370 406 462
Contingence, Angle of      see Angle.
Cox, Homersham      346 370 399 400 401 575
Cubics, Linear Construction of      233 sqq.
Curl, defined      554;
Curl, Flux, defined      554;
Curl, Lines and Filaments, defined      567
Curvature of Curves and Surfaces in Euclidean Space      544 sqq
Curvature of Curves and Surfaces in Non-Euclidean Space      479 sqq
Curve-Locus in Space of v Dimensions, defined      130;
Curve-Locus, Quadriquadric      144 151.
Curvilinear Locus in Space of » Dimensions, defined      130
Cylindroid in Euclidean Space      532;
Cylindroid in Non-Euclidean Soace      403
De Morgan      32 100 122 131
Dependence in a Positional Manifold, defined      123.
Derivation, General Definition of      8.
Determinants and Combinatorial Multiplication      180;
Determinants, associated with Matrices      252.
Determining Property of a Scheme      8.
Developable Surface in Non-Euclidean Geometry      481.
Development in the Algebra of Symbolic Logic      45 sqq.
Diametral Plane of a Dual Group in Euclidean Space      532.
Differential, distinguished from Universal Algebra      18 sqq.
Dimensions of a Manifold, denned      17
Direct Transformation of a Quadric      338 sqq.;
Direct Transformation of the Absolute      456 sqq
Director Force, Line, or Equation, of a Group      286 sqq.
Discourse, Universe of      100
Discriminants of Equations, defined and discussed      51 sqq.;
Discriminants of Sub sumptions, denned      59
Disjunctive Complex      107 sqq
Displacements of Bigid Bodies in Euclidean Space      500 sqq. 536;
Displacements of Bigid Bodies in Non-Euclidean Space      456 sqq.;
Displacements Vector      472 sqq
Displacements, Small      464 476;
Displacements, Surfaces of Equal      462 472;
Distance in Elliptic Geometry, Shortest      385 387
Distance in Hyperbolic Geometry      416 sqq.;
Distance in Hyperbolic Geometry between Planes      428
Distance in Hyperbolic Geometry, Angular between Points      417
Distance in Hyperbolic Geometry, Shortest      429 sqq.;
Distance in Non-Euclidean Geometry between Sub-regions      365 sqq.;
Distance in Non-Euclidean Geometry between Sub-regions, Definition of      352
Distance, General Theory of      349 sqq.;
Distributive Law in Algebra of Symbolic Logic      37 84 174.
Divergence, defined      554
Division in Algebra of Space in Non-Euclidean Geometry      355 379.
Division in Algebra of Symbolic Logic      80 sqq.
Dual group      see Group.
Duality, Theory of      147 196 481
Dupin's Theorem in Euclidean Space      546;
Dupin's Theorem in Non-Euclidean Space      494.
Elements and Terms      21
Elements and Terms, Antipodal      166 361
Elements and Terms, Co-ordinate      125
Elements and Terms, Intensively Imaginary      166;
Elements and Terms, Intensively Imaginary, Real      166
Elements and Terms, Linear, defined      177;
Elements, Linear, in Euclidean Space      508 sqq.;
Elements, Linear, in Non-Euclidean Space      399 sqq. 452
Elements, Linear, in Positional Manifold, and Mechanical Forces      273
Elements, Null, in Symbolic Logic      35 37 38;
Elements, of a Manifold, defined      13;
Elements, of a Manifold, Secondary Properties of      14
Elements, Planar, denned      177
Elements, Regional, defined      177
Elements, Self-Normal      204 sqq.
Elements, Spatial and Antispatial, in Hyperbolic Space      414 sqq.
Elements, Supplementary, in Symbolic Logic      36 sqq
Elimination and Syllogisms      103 sqq.;
Elimination and Syllogisms from Existential Expressions      89 sqq.
Elimination and Syllogisms in Symbolic Logic, defined and discussed      47 sqq.;
Elimination and Syllogisms in Symbolic Logic, Formula for      55.
Elliptic Definition of Distance      352
Elliptic Space, Formulae for      356 sqq.
Elliptic Space, Kinematics of      470 sqq.
Elliptic Space, Parallel Lines in      404 407
Elliptic Space, Parallel Lines in Subregions in      397 sqq.
Elliptic Space, Vector Systemsof Forces in      406 sqq.
Elliptic Space, Vector Systemsof Forces in, Transformations in      472 sqq.
Elliptic Spatial Manifold, defined      355
Engel, F.      317 369 370 573
Equal Displacement, Surface of      462 472
Equations in Algebra of Symbolic Logic, viz. and Universal Propositions      105;
Equations in Extensive and Positional Manifolds      viz.
Equations of Condition, defined      172
Equations of Subregions      195
Equations with many Unknowns      52
Equations with many Unknowns, Discriminants of      53
Equations with many Unknowns, Resultants of      53;
Equations, Auxiliary      71 78;
Equations, Defining, denned      162
Equations, Director, of Groups      286
Equations, Identical of Matrices      256 261;
Equations, Limiting and Unlimiting, defined      59;
Equations, Negative and Positive Constituents of, defined      50
Equations, Plane and Point      147
Equations, Reciprocal, defined      147
Equations, simultaneous      51 sqq.;
Equations, Simultaneous, Discriminants of, defined      52;
Equations, Simultaneous, Resultant of, denned      52
Equations, with many Unknowns, Johnson's Method      73 sqq.
Equations, with many Unknowns, Skew-Symmetrical      71 sqq.
Equations, with many Unknowns, Solution      65 sqq.
Equations, with many Unknowns, Symmetrical      67 sqq. 73 75
Equations, with one Unknown      49 sqq.;
Equations, with one Unknown, Discriminants of      51
Equations, with one Unknown, Resultant of      51
Equations, with one Unknown, Solution of      55
Equations, with one Unknown, Standard Form of      49
Equivalence, defined      5;
Equivalence, Definition concerning, in Universal Algebra      18;
Equivalence, in Symbolic Logic, for Propositions      108
Equivalence, in Symbolic Logic, interpreted      38
Equivalence, in Symbolic Logic, Proof of      36.
Euler's Theorem, in Euclidean Geometry      547;
Euler's Theorem, in Non-Euclidean Geometry      492.
Existential Expressions      83 sqq.
Existential Expressions and Propositional Interpretation      111 sqq.;
Existential Expressions, Resultant of, denned      90
Existential Expressions, Solution of      91.
Expressions, Field of, defined      60
Extension of Field, maximum and minimum, defined      61.
Extension, Calculus of, investigated      169 sqq.;
Extension, Calculus of, mentioned      28 31 132 146
Extensive Magnitudes, defined      176 sqq.;
Extensive Manifolds and Non-Euclidean Geometry      399 sqq. 452
Extensive Manifolds and Non-Euclidean Geometry of three dimensions      273 sqq.
Extensive Manifolds and Non-Euclidean Geometry, defined      177;
Extraordinaries, defined      119*
Field of an Expression, defined      60;
Field of an Unknown, defined      60
Field, Limited, defined      61;
Flow of a Vector, defined      572.
Flux, defined for Point and Vector Formulas      527;
Flux, defined for Pure Vector Formulae      549;
Flux, Multiplication      528 sqq.;
Flux, Operation of Taking the      522 527
Flye, Ste Marie      369
Force, defined      177;
Force, defined, Compared with Mechanical Force      273;
Force, defined, Single, Condition for      277
Forces, Director, of a Group      286;
Forces, Groups of Systems of      see Groups;
Forces, Intensity of, in Euclidean Space      525
Forces, Intensity of, in Non-Euclidean Space      399 452;
Forces, Investigated      273 sqq.;
Forces, Spatial, investigated      452 sqq.;
Forces, Systems of      see Systems.
Forsyth      17 573
Franklin, Mrs      98 116
Frischauf      369
Functions, Theory of      11
Gauss      488 490 543.
Generating Begions of Quadrics      147 sqq. 152
Generating Begions of Quadrics in Non-Euclidean Geometry      397 451.
Generators, Positive and Negative Systems of      207
Geometry and Algebra      11;
Geometry and Extensive Manifolds      273
Geometry of a Sphere, Euclidean      365
Geometry, Descriptive, and Calculus of Extension      214;
Geometry, Descriptive, and Calculus of many Dimensions      131
Geometry, Elliptic, Polar and Antipodal Forms, defined      355;
Geometry, Hyperbolic, Investigated      414 sqq.
Geometry, Line-      278;
Geometry, Non-Euclidean, and Cayley's Theory of Distance      351
Geometry, Non-Euclidean, and Lindemann's Theory of Forces      281;
Geometry, Non-Euclidean, Historical Note upon      369 sqq.
Geometry, Parabolic      496 sqq.
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